In this paper, we study the spread of virus/worm in computer
networks with a view to addressing cyber security problems. Epidemic
models have been applied extensively to model the propagation of
computer viruses, which characterize the fact that infected machines
may spread malware to other hosts connected to the network. In our
framework, the dynamics of hosts evolves according to a modified
inhomogeneous Susceptible-Infectious-Susceptible (SIS) epidemic
model with time-varying transmission rate and recovery rate. The
infection of computers is subject to direct attack as well as
propagation among hosts. Based on optimal control theory, optimal
attack strategies are provided by minimizing the cost (equivalently
maximizing the profit) of the attacker. We present a threshold
function of the fraction of infectious hosts, which captures the
dynamically evolving strategies of the attacker and reflects the
persistence of virus spreading. Moreover, our results indicate that
if the infectivity of a computer worm is low and the computers are
installed with antivirus software with high reliability, the
intensity of attacks incurred will likely be low. This agrees with
our intuition.